Work

Dynamic sparse physics-aware network for solving partial differential equations on multiple grid types

Year: 2025

Type: article

Abstract: Neural network have been widely applied for solving partial differential equations (PDEs), but they still exhibit limitations. Recently, transformer-based operators, which have demonstrated exceptional performance in fields like computer vision, have been adapted for PDE solving. We propose a dynamic sparse physics-aware network (DSPAN) based on a physics-slicing mechanism and a TopK selection architecture. First, the input features are partitioned into slices to capture the intrinsic physical states. Then, these slices are scored for importance, and only the top K most critical slices are selected for attention computation. This architecture effectively captures the underlying physical information in PDEs while improving computational efficiency, achieving dual gains in both accuracy and speed. Experiments show that DSPAN achieves a relative improvement 15.35% on eight benchmark data sets, with a particularly notable 33% enhancement in plasticity equations. This robustly validates the algorithm’s capability to deliver highly accurate and resource-efficient solutions for complex PDE systems.

Source: Machine Learning Science and Technology

DOI: 10.1088/2632-2153/ae2740

Authors: Xichen Cao, Peizhi Zhao, Qinglong Ma, Tao Song

Institution: China University of Petroleum, East China

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,000

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province